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| JFZ5220 | Inversion Method in Geophysics | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of GEOPHYSICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Hüseyin GÖKALP | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The student should obtain fundamental and advanced knowledge about inverse problems in geophysics. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | appraisal the general philosophy of the inverse theory | 1,2,3 | 1,4 | | PO - 2 : | help the student to understand and discuss various inverse problems and their solutions. | 1,2,3 | 1,4 | | PO - 3 : | appreciate how to solve geophysical data with inversion methods | 1,2,3 | 1,4 | | PO - 4 : | develop the students interpretation and modelling (forward and inverse) abilities on geophysical data. | 1,2,3 | 1,4 | | PO - 5 : | enhance the level a knowledge of linear algebra, matrix solution of linear and non-linear equation systems | 1,2,3 | 1,4 | | PO - 6 : | discuss and evaluate the resolution parameters of inversion results. | 1,2,3 | 1,4 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Describing the forward and inverse problem. Determination of the structural parameters. Analysis of error. L1, L2 norm criteria. Backus-Gilbert method. Maximum likelihood method. Stochastic inverse. Generalized inverse. Damped least square method. Marquardt-Levenberg method. Inversion in model space and data space. Null space problem. Singular value decomposition. Analysis of resolution. Linear and nonlinear problems. Mixed-determined and under-determined systems and their possible solutions. Linearizable problems. Assessment the results of the inversion: model and data resolution matrix. kovariance matrix. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Short history. Introduction of the inversion theory. | | | Week 2 | Introduction forward and inverse problem and their relationship. | | | Week 3 | Overview of the modelling methods. Determination of the structural parameters. | | | Week 4 | L1 and L2 norm solutions. Overview linear algebra. | | | Week 5 | Singular Value Decomposition. Importance of the singular value in the inversion. | | | Week 6 | Backus-Gilbert technique. | | | Week 7 | Linear and nonlinear problem. Stochastic inversion method. | | | Week 8 | Mid-term exam | | | Week 9 | Marquardt-Levenberg method. Generalized inverse method. | | | Week 10 | Backus-Gilbert method. | | | Week 11 | Maximum likelihood method. Mixed- and Under- determined systems and their solutions | | | Week 12 | Linearization of the nonlinear system and their inversion process. | | | Week 13 | Investigation of the inversion results. Model and data resolution matrix. Covarians matrix. | | | Week 14 | Computer modelling a geophysical problem (e.g. an example of seismic tomography) and obtaining its forward solution.Estimation of the model parameters (earth structure) computer application on the synthetic data obtained form forward solution.Assessment of the inversion results by using computer. Obtaining model resolution matrix and data resolution matrix. Inverstigation of the data noise on the parameter estimation. | | | Week 15 | Make-up lesson | | | Week 16 | End-of-term exam | | | |
| 1 | Menke. W. 1989, Geophysical Data Analaysis: Discrete Inverse Theory, Academic Pres | | | 2 | Aster, R. 2000, Geohysical Inverse Theory, Class Notes | | | |
| 1 | Aki, K. And Richards, P.G., 1980, Quantitative Seismology, W.H. Freeman and Company,1980 | | | 2 | Claerbout, J., 1985. Imaging the Earths Interior, Blackwell Scientific.Claerbout, J., 1992. Earth Sounding Analysis, Blackwell Scientific. | | | 3 | Tarantola, A., 1987, Inverse Problem Theory, Elsevier, Amsterdam | | | 4 | Parker, R. 1994, Geophysical Inverse Theory, Princeton University Press.. | | | 5 | Lanczos, C. 1961, Linear Differential Operators, Van Nostrand-Reinhold. | | | 6 | Scales, J.A., 1997, Theory of Seismic Imaging, SAMIZDAT Pres, Golden, Co.Scales, J.A., and M.L. Smith, 1997, Introductory Geophysical Inverse Theory, SAMIZDAT Pres, Golden, Co. | | | 7 | Iyer, H.M., and K. Hirahara (Eds.), 1993. Seismic Tomography Theory and Practice, Chapman Hall, New York. | | | 8 | Başokur, A. T., Doğrusal ve Doğrusal Olmayan Problemlerin Ters-Çözümü, TMMOB Jeofizik Müh. Odası Eğitim Yayınları, No:4 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 14/05/2010 | 1,50 | 30 | | In-term studies (second mid-term exam) | 12 | 12/05/2010 | 1,30 | 20 | | End-of-term exam | 16 | 09/06/2011 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Sınıf dışı çalışma | 4 | 14 | 56 | | Laboratuar çalışması | 3 | 4 | 12 | | Ödev | 6 | 6 | 36 | | Total work load | | | 104 |
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